Displacement washing is a common process to improve product quality in a filtration process. The filter cake is permeated with a wash liquid, displacing dissolved substances from its pores. In industrial washing processes, the wash liquid is usually applied to the cake surface via spray nozzles, drip plates or overflow channels. In order to distribute the liquid homogeneously, a wash liquid supernatant is usually formed to cover the whole cake surface. The mechanical impact of the wash liquid causes the filter cake to be partially reslurried, which allows impurities from the pores to enter the supernatant and contaminate the wash liquid even before it penetrates the cake. This wash liquid contamination limits the result of displacement washing.

In recent publications by the authors, it has been shown that the extent of partial cake reslurrying can be described quantitatively using the cake reslurry ratio φ as a dimensionless and intuitive parameter. The cake reslurry ratio φ can be determined experimentally by analyzing the supernatant concentration. In this paper, a model is presented to predict the best possible washing result due to the negative effects of partial cake reslurrying based on an analysis of the contaminated supernatant. Model predictions are validated using experimentally determined wash curves. The supernatant contamination caused by partial cake reslurrying is identified as a previously undescribed limiting effect for displacement washing.

The presented model approach forms an analogy to established theories of dilution washing and can be used to describe wash limits due to partial cake reslurrying for displacement washing. This closes a gap between two of the most common washing processes and opens a new perspective for the evaluation of displacement washing results. A generalized evaluation to describe the influence of wash liquid interactions with the cake surface is enabled which provides an important approach for the optimization of washing processes. As a result, unforeseen process deviations can be identified at an early stage of process design, leading to the reduction of investment, operating and downstream processing costs.